Question

An object was dropped off the top of a building. The function f(x) = -16x² + 144 represents the height of the object above the ground, in feet, a seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function. Answer Attempt 1 out of 2 f(-2) = meaning that above the ground. This interpretation f(1.5) = meaning that above the ground. This interpretation f(4) = meaning that above the ground. This interpretation seconds after the object was dropped, the object was in the context of the problem. seconds after the object was dropped, the object was in the context of the problem. V seconds after the object was dropped, the object was v in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is feet 团 feet feet​

Answer 1

Explanation:

We have f(x) = 144 - 16x², where f(x) represents the height of the object above the ground x seconds after being dropped.

Clearly, we have x ≥ 0. Moreover, we have f(x) ≥ 0.

=> 144 - 16x² ≥ 0

=> 16x² ≤ 144

=> x² ≤ 9

=> -3 ≤ x < 0 (rej.) or 0 ≤ x ≤ 3.

Hence, an appropriate domain is [0, 3].

Answer 2

Appropriate domain for the function is x is for all real numbers.

Explanation:

Interpretation of f(-2):

f(-2) = -16(-2)² + 144 = 89

This means that after -2 seconds, the object was 80 feet above the ground.

Interpretation of f(1.5):

f(1.5) = -16(1.5²) + 144 = 108

This means that after 1.5 seconds, the object was 108 feet above the ground.

Interpretation of f(4):

f(4) = -16(4²) + 144 = -112

This means that after 4 seconds, the object was -112 feet above the ground.

Appropriate domain for the function:

The function f(x) = -16x² + 144 represents the height of an object above the ground, regardless of whether the object is falling or rising.

Therefore, the domain of the function is all real numbers.

Observations:

• After -2 seconds, the object is above the ground, which is reasonable because the object is still falling.
• After 1.5 seconds, the object is still above the ground, but it is getting closer to the ground.
• After 4 seconds, the object is below the ground, which is reasonable because the object has reached the ground and has fallen below it.

Based on these observations, it is clear that an appropriate domain for the function is x is for all real numbers.